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<p>Users need more efficient and more secure  when they use the Internet. Password authentication code (PAC) is the critical issue in many applications such as web-sites and data base systems etc. In this paper, PAC between two users to confirm authentication between them based two factors has presented.. Two factors is the most good solution in this field. A legitimate user needs to make sure about his partner to ensure their communication.  So, this solution produces two important algorithms, the first one is utilized the Diffie-Hellman which considered the base of this work. The second is routing in message passing networks<strong><em> </em></strong>(RMPN) algorithm which determine the positions of bits which sent to specific party. The overall of this method convincingly to be more secure against both online and offline attacks. This scheme has some advantages such as secrecy of session key, password privacy, and mutual authentication. The performance and security analyses prove that the scheme is very efficient and mathematically immune for attackers.</p>

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Many applications in the internet using Password for identify users.  So, this password must be strong and safe to avoid unauthorized users. The critical issue in many applications such as web-sites and data base systems is password authentication code (PAC). In this paper, PAC between two parties to confirm password authentication between them based mutual text authentication has presented. Two factors is the best solution in this field. But to be more secure and to be more efficient a legitimate user needs to make sure about his partner to ensure their communications should use another method without need more costs and avoid plurality of algorithms.  So, this solution uses mutual text authentication as new solution which the text is predetermined by users. This method is considered new in this field, as this method tries to make the password highly secure in front of unauthorized users and to make the process of accessing information specific only to the actual authorized users. When analysing this method, we find that it has many characteristics such as the confidentiality of the session key and privacy, in addition to the exchange of authentication between the two parties to ensure that others do not interfere.